That's sort of what I'm thinking. Of course i'd rather not waste the money on a pile of rejections....but I can afford too if that's the case(just not happily;) ). Also, I just discovered this website yesterday, and since posting my original questions, I've done a little more reading. i think that I gave the impression that I'm shooting a little higher than I really am. My definition of second tier included the top 40 or so, but it seems like it's more commonly used to describe the top 20ish? The list of schools I'm considering giving a shot at (give or take a few) are: Chicago, UCLA, U-Mich, UCSD, Maryland, BU, Brown, UT-Austin, UC Davis, BC, Georgetown, and Colorado. I'm well aware that Chicago(really the only reason I'm even considering giving it a try is because one of my recommenders went there and seems to think that because its easier to get in than out, they might be willing to give me a shot), UCLA, U-Mich are big reaches and my lack of real analysis will almost certainly keep me out. However, I'm concerned that it will keep me out of the rest as well. Thanks again for all your help....I only wish I found this site earlier!